In a farm, some keepers have 30 cows,50 hens and 23 goats. If total no of legs be 224 more then the number of heads in the farm. Find the number of keepers

Options

A. 5
B. 8
C. 10
D. 15

Answer

To solve the problem step by step, let's break down the information given and calculate the required values.

### Step 1: Identify the number of animals and their legs
- **Cows**: 30 cows, and each cow has 4 legs.
- **Hens**: 50 hens, and each hen has 2 legs.
- **Goats**: 23 goats, and each goat has 4 legs.

### Step 2: Calculate the total number of legs from the animals
- Total legs from cows = 30 cows × 4 legs/cow = 120 legs
- Total legs from hens = 50 hens × 2 legs/hen = 100 legs
- Total legs from goats = 23 goats × 4 legs/goat = 92 legs

Now, let's sum these up:
- Total legs from animals = 120 + 100 + 92 = 312 legs

### Step 3: Calculate the total number of heads
- Each animal (cows, hens, goats) has 1 head.
- Total heads from cows = 30 heads
- Total heads from hens = 50 heads
- Total heads from goats = 23 heads
- Total heads from keepers = X heads (where X is the number of keepers)

Now, let's sum these up:
- Total heads = 30 + 50 + 23 + X = 103 + X heads

### Step 4: Set up the equation based on the problem statement
According to the problem, the total number of legs is 224 more than the total number of heads:
\[ \text{Total legs} = \text{Total heads} + 224 \]
Substituting the values we calculated:
\[ 312 + 2X = 103 + X + 224 \]

### Step 5: Simplify the equation
Now, let's simplify the equation:
1. Combine like terms:
\[ 312 + 2X = 327 + X \]
2. Rearranging gives:
\[ 2X - X = 327 - 312 \]
\[ X = 15 \]

### Conclusion
The number of keepers is **15**.